package com.thealgorithms.datastructures.bloomfilter;
import java.util.BitSet;
public class BloomFilter<T> {
private int numberOfHashFunctions;
private BitSet bitArray;
private Hash<T>[] hashFunctions;
public BloomFilter(int numberOfHashFunctions, int n) {
this.numberOfHashFunctions = numberOfHashFunctions;
hashFunctions = new Hash[numberOfHashFunctions];
bitArray = new BitSet(n);
insertHash();
}
private void insertHash() {
for (int i = 0; i < numberOfHashFunctions; i++) {
hashFunctions[i] = new Hash(i);
}
}
public void insert(T key) {
for (Hash<T> hash : hashFunctions){
int position = hash.compute(key) % bitArray.size();
bitArray.set(position);
}
}
public boolean contains(T key) {
for (Hash<T> hash : hashFunctions){
int position = hash.compute(key) % bitArray.size();
if (!bitArray.get(position)) {
return false;
}
}
return true;
}
private class Hash<T> {
int index;
public Hash(int index){
this.index = index;
}
public int compute(T key){
return index * asciiString(String.valueOf(key));
}
private int asciiString(String word){
int number = 0;
for (int i=0;i<word.length();i++){
number += word.charAt(i);
}
return number;
}
}
}
Bloom Filters are one of a class of probabilistic data structures. The Bloom Filter uses hashes and probability to determine whether a particular item is present in a set. It can do so in constant time: O(1) and sub-linear space, though technically still O(n). An important feature of a Bloom Filter is that it is guaranteed never to provide a false negative, saying an element isn't present when it is. However, it has a probability (based on the tuning of its parameters) of providing a false positive, saying an element is present when it is not. The Bloom Filter uses a multi-hash scheme. On insertion, the inserted object is run through each hash, which produces a slot number. That slot number is flipped to 1 in the bit array. During a presence check, the object is run through the same set of hashes, and if each corresponding slot is 1, the filter reports the object has been added. If any of them are 0, it reports that the object has not been added. The hashes must be deterministic and uniformly distributed over the slots for the Bloom filter to operate effectively.
Operation | Average |
---|---|
Initialize | O(1) |
Insertion | O(1) |
Query | O(1) |
Space | O(n) |
k
), and with an array of bits of size M
with each bit set to 0. There are 3 distinct schemes to tune these parameters.
M
and k
are explicitly set by the userk
and M
are calculated based off the expected number of elements to minimize false positives.k
and M
are calculated based off a desired error rate.k
hashesn
determine the slot within the filter m
by calculating n % M = m
m
within the filter to 1k
hashesn
determine the slot within the filter m
by calculating n % M = m
m
, if m
is set to 0 return falseAs an example, let us look at a Bloom Filter of Strings, we will initialize the Bloom Filter with 10 slots an we will use 3 hashes
slot | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
state | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Let's try to insert foo
, we will run foo
through our three hash functions
h1(foo) = 2
h2(foo) = 5
h3(foo) = 6
With hashes run, we will flip the corresponding bits to 1
slot | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
state | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
Let's first try querying bar
, to query bar
we run bar
through our three hash functions:
h1(bar) = 3
h2(bar) = 4
h3(bar) = 6
If we look at our bit array, bits 3 and 4 are both not set, if even just 1 bit is not set, we return false, so in this case we return false. bar
has not been added
Let's now try to query foo
, when we run foo
through our hashes we get:
h1(foo) = 2
h2(foo) = 5
h3(foo) = 6
Of course, since we already inserted foo, our table has each of the three bits our hashes produced set to 1, so we return true, foo
is present
Let's say we inserted bar
and the current state of our table is:
slot | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
state | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
Let's now query baz
, when we run baz through our hash functions we get:
h1(baz) = 3
h2(baz) = 5
h3(baz) = 6
Notice that this does not match either the result of foo
or bar
, however because slots 3, 5, and 6 are already set, we report true, that baz is in the set, and therefore produce a false positive.
The probability of false positives increases with the probability of hash collisions within the filter. However, you can optimize the number of collisions if you have some sense of the cardinality of your set ahead of time. You can do this by optimizing k
and M
, M
should be ~ 8-10 bits per expected item, and k
should be (M/n) * ln2
.
Implementations of the Bloom Filter are available for: